The nature of the relationship between box-and-arrow (BA) explanations and neuroscientific mechanism descriptions (NMDs) is a key foundational issue for cognitive science. In this article we attempt to identify the nature of the constraints imposed by BA explanations on the formulation of NMDs. On the basis of a case study about motor control, we argue that BA explanations and NMDs both identify regularities that hold in the system, and that these regularities place constraints on the formulation of NMDs from BA analyses, and vice versa. The regularities identified in the two kinds of explanation play a crucial role in reasoning about the relationship between them, and in justifying the use of neuroscientific experimental techniques for the empirical testing of BA analyses of behavior. In addition, we make claims concerning the similarities and differences between BA analyses and NMDs. First, we argue that both types of explanation describe mechanisms. Second, we propose that they differ in terms of the theoretical vocabulary used to denote the entities and properties involved in the mechanism and engaging in regular, mutual interactions. On the contrary, the notion of abstractness, defined as omission of detail, does not help to distinguish BA analyses from NMDs: there is a sense in which BA analyses are more detailed than NMDs. In relation to this, we also focus on the nature of the extra detail included in NMDs and missing from BA analyses, arguing that such detail does not always concern how the system works. Finally, we propose reasons for doubting that BA analyses, unlike NMDs, may be considered “mechanism sketches.” We have developed these views by critically analyzing recent claims in the philosophical literature regarding the foundations of cognitive science.